Cole's L'Oreal TV ad, which launched on 9 October, features the Girls Aloud singer praising the Elvive Full Restore 5 shampoo and conditioner range.
She says: "My hair feels stronger, full of life, replenished with a healthy shine. It's got its mojo back."
Cole, who landed the contract to front the beauty brand in August this year, is known to use artificial hair extensions made from acrylic. Her hairdresser, Julien Guyonnet, told The Sunday Times that he last put extensions into her locks four weeks ago and before that, had given her fibre hair extensions in July.
The pop star's extensions are noted during the 30-second spot when a message appears that says "styled with some natural extensions", however it appears on screen for only two seconds.
Fans were annoyed that Cole does not mention the hair extensions herself.
Daisy Goodwin, a television producer and occasional Sunday Times columnists, was among those that complained to the ASA, claiming the ad was misleading.
The ASA ruled that the ad did not break any rules and in its explanation to Goodwin wrote: "A problem would only arise if the ad did not make clear that [Cole] is wearing these extensions."